Relativistic Expansion of Magnetic Loops at the Self-similar Stage

Details Relativistic Expansion of Magnetic Loops at the Self-similar Stage Relativistic Expansion of Magnetic Loops at the Self-similar Stage

2008-12-10

arxiv.org/abs/0812.1909v2

Astronomy and Astrophysics

Astrophysics

23 pages, 36 figures, accepted for publication in MNRAS. We revised our manuscript in equation (67). This change does not affe

Scientific paper

10.1111/j.1365-2966.2008.14357.x

We obtained self-similar solutions of relativistically expanding magnetic loops taking into account the azimuthal magnetic fields. We neglect stellar rotation and assume axisymmetry and a purely radial flow. As the magnetic loops expand, the initial dipole magnetic field is stretched into the radial direction. When the expansion speed approaches the light speed, the displacement current reduces the toroidal current and modifies the distribution of the plasma lifted up from the central star. Since these self-similar solutions describe the free expansion of the magnetic loops, i.e., $Dv/Dt=0$, the equations of motion are similar to those of the static relativistic magnetohydrodynamics. This allows us to estimate the total energy stored in the magnetic loops by applying the virial theorem. This energy is comparable to that of the giant flares observed in magnetars.

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